Curriculum
Mutuazione: 20410408 AL310 - ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L-35 CAPUANO LAURA, TALAMANCA VALERIO
Programme
Fields extensions and their basic properties.Algebraic closure of a field: existence and uniqueness. Kronecker's construction.
Splitting fields and normal extensions.
Separable, inseparable and purely inseparable extensions. Primitive element theorem.
Galois extensions. Galois group and Galois correspondence for finite extensions.
Prefinite groups and Krull topology. Galois correspondence for infinite extensions.
Galois group of an equation. Cyclotomic extensions. Generic equation of degree n.
Linear independence of characters. Trace and norm. Hilbert 90 theorem. Cyclic extensions and Kummer theory.
Solvable groups. Solvable and solvable by radicals extensions.
More examples and applications.
Core Documentation
Algebra S. BoschAlgebra S. Lang
Algebra M. Artin
Class Field Theory J. Neukirch
Type of delivery of the course
Lectures in class on blackboard and exercise classes. The students should enroll in the course on Moodle and Teams. The communications will be held through these channels.Type of evaluation
The exam will consist of a written and an oral exam of the topics studied in the course.Mutuazione: 20410408 AL310 - ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L-35 CAPUANO LAURA, TALAMANCA VALERIO
Mutuazione: 20410408 AL310 - ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L-35 CAPUANO LAURA, TALAMANCA VALERIO
Programme
Fields extensions and their basic properties.Algebraic closure of a field: existence and uniqueness. Kronecker's construction.
Splitting fields and normal extensions.
Separable, inseparable and purely inseparable extensions. Primitive element theorem.
Galois extensions. Galois group and Galois correspondence for finite extensions.
Prefinite groups and Krull topology. Galois correspondence for infinite extensions.
Galois group of an equation. Cyclotomic extensions. Generic equation of degree n.
Linear independence of characters. Trace and norm. Hilbert 90 theorem. Cyclic extensions and Kummer theory.
Solvable groups. Solvable and solvable by radicals extensions.
More examples and applications.
Core Documentation
Algebra S. BoschAlgebra S. Lang
Algebra M. Artin
Class Field Theory J. Neukirch
Type of delivery of the course
Lectures in class on blackboard and exercise classes. The students should enroll in the course on Moodle and Teams. The communications will be held through these channels.Type of evaluation
The exam will consist of a written and an oral exam of the topics studied in the course.Mutuazione: 20410408 AL310 - ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L-35 CAPUANO LAURA, TALAMANCA VALERIO
Mutuazione: 20410408 AL310 - ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L-35 CAPUANO LAURA, TALAMANCA VALERIO
Programme
Fields extensions and their basic properties.Algebraic closure of a field: existence and uniqueness. Kronecker's construction.
Splitting fields and normal extensions.
Separable, inseparable and purely inseparable extensions. Primitive element theorem.
Galois extensions. Galois group and Galois correspondence for finite extensions.
Prefinite groups and Krull topology. Galois correspondence for infinite extensions.
Galois group of an equation. Cyclotomic extensions. Generic equation of degree n.
Linear independence of characters. Trace and norm. Hilbert 90 theorem. Cyclic extensions and Kummer theory.
Solvable groups. Solvable and solvable by radicals extensions.
More examples and applications.
Core Documentation
Algebra S. BoschAlgebra S. Lang
Algebra M. Artin
Class Field Theory J. Neukirch
Type of delivery of the course
Lectures in class on blackboard and exercise classes. The students should enroll in the course on Moodle and Teams. The communications will be held through these channels.Type of evaluation
The exam will consist of a written and an oral exam of the topics studied in the course.Mutuazione: 20410408 AL310 - ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L-35 CAPUANO LAURA, TALAMANCA VALERIO